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An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…

Mathematical Physics · Physics 2015-06-16 Leonardo Colombo , David Martín de Diego , Marcela Zuccalli

In this paper, we present a method that enables solving in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

Optimization and Control · Mathematics 2012-03-13 Yvon Maday , Mohamed-Kamel Riahi , Julien Salomon

This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form…

Optimization and Control · Mathematics 2024-10-01 Cung The Anh , Nguyen Hai Ha Giang

The autor considers an initial-boundary value problem for the nonstationary Stokes system in an angle, where Dirichlet and Neumann conditions are prescribed on the diferent sides of the angle. The major part of the paper deals with the…

Analysis of PDEs · Mathematics 2025-03-25 Jürgen Rossmann

In this paper, we study a class of fractional optimal control problems. A necessary condition for the existence of an optimal control is provided in the literature. It is commonly given as the existence of a solution of a fractional…

Optimization and Control · Mathematics 2012-03-08 Loïc Bourdin

The main contributions of this paper are three fold. First, our primary concern is to investigate a class of stochastic recursive delayed control problems which arise naturally with sound backgrounds but have not been well-studied yet. For…

Optimization and Control · Mathematics 2011-12-06 Li Chen , Jianhui Huang

We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are…

Optimization and Control · Mathematics 2007-05-23 Delfim F. M. Torres

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an…

Probability · Mathematics 2017-05-12 Jiaqiang Wen , Yufeng Shi

In this paper, we solve an open problem and obtain a general maximum principle for a stochastic optimal control problem where the control domain is an arbitrary non-empty set and all the coefficients (especially the diffusion term and the…

Optimization and Control · Mathematics 2023-02-08 Weijun Meng , Jingtao Shi , Tianxiao Wang , Ji-Feng Zhang

We study dynamic minimization problems of the calculus of variations with generalized Lagrangian functionals that depend on a general linear operator $K$ and defined on bounded-time intervals. Under assumptions of regularity, convexity and…

Optimization and Control · Mathematics 2014-05-08 Loïc Bourdin , Tatiana Odzijewicz , Delfim F. M. Torres

We derive the equations of motion of an action-dependent version of the Einstein-Hilbert Lagrangian, as a specific instance of the Herglotz variational problem. Action-dependent Lagrangians lead to dissipative dynamics, which cannot be…

General Relativity and Quantum Cosmology · Physics 2023-03-08 Jordi Gaset , Arnau Mas

We develop Cresson's non-differentiable embedding to quantum problems of the calculus of variations and optimal control with time delay. Main results show that the dynamics of non-differentiable Lagrangian and Hamiltonian systems with time…

Optimization and Control · Mathematics 2013-06-13 Gastao S. F. Frederico , Delfim F. M. Torres

We consider problems of the calculus of variations on unbounded time scales. We prove the validity of the Euler-Lagrange equation on time scales for infinite horizon problems, and a new transversality condition.

Optimization and Control · Mathematics 2011-01-04 Agnieszka B. Malinowska , Natalia Martins , Delfim F. M. Torres

We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay…

Dynamical Systems · Mathematics 2022-07-27 N. I. Mahmudov

Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…

Optimization and Control · Mathematics 2017-02-08 Leonardo Colombo

We present here the classical Schwarz method with a time domain decomposition applied to unconstrained parabolic optimal control problems. Unlike Dirichlet-Neumann and Neumann-Neumann algorithms, we find different properties based on the…

Numerical Analysis · Mathematics 2024-08-23 Martin Jakob Gander , Liu-Di Lu

In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target…

Numerical Analysis · Mathematics 2025-03-24 Luise Blank

We introduce a discrete-time fractional calculus of variations on the time scales $\mathbb{Z}$ and $(h\mathbb{Z})_a$. First and second order necessary optimality conditions are established. Some numerical examples illustrating the use of…

Classical Analysis and ODEs · Mathematics 2012-02-15 Nuno R. O. Bastos

In this paper, we present a method that enables to solve in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

Optimization and Control · Mathematics 2011-10-19 Yvon Maday , Julien Salomon , Kamel Riahi

We extend Noether's theorem to dynamical optimal control systems being under the action of nonconservative forces. A systematic way of calculating conservation laws for nonconservative optimal control problems is given. As a corollary, the…

Optimization and Control · Mathematics 2007-05-23 Gastao S. F. Frederico , Delfim F. M. Torres